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Kaczmarz algorithm in Hilbert space

Rainis Haller, Ryszard Szwarc (2005)

Studia Mathematica

The aim of the Kaczmarz algorithm is to reconstruct an element in a Hilbert space from data given by inner products of this element with a given sequence of vectors. The main result characterizes sequences of vectors leading to reconstruction of any element in the space. This generalizes some results of Kwapień and Mycielski.

Kaczmarz algorithm with relaxation in Hilbert space

Ryszard Szwarc, Grzegorz Świderski (2013)

Studia Mathematica

We study the relaxed Kaczmarz algorithm in Hilbert space. The connection with the non-relaxed algorithm is examined. In particular we give sufficient conditions when relaxation leads to the convergence of the algorithm independently of the relaxation coefficients.

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